SET007 Axioms: SET007+599.ax


%------------------------------------------------------------------------------
% File     : SET007+599 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Propositional Calculus for Boolean Valued Functions. Part IV
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : bvfunc_8 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   29 (   0 unit)
%            Number of atoms       :  125 (  26 equality)
%            Maximal formula depth :   11 (   8 average)
%            Number of connectives :  125 (  29 ~  ;   0  |;   0  &)
%                                         (   0 <=>;  96 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    4 (   0 propositional; 1-4 arity)
%            Number of functors    :   10 (   1 constant; 0-3 arity)
%            Number of variables   :   96 (   0 singleton;  96 !;   0 ?)
%            Maximal term depth    :    6 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k14_bvfunc_1(A,B,k6_valuat_1(A,k6_valuat_1(A,C,D),E)) = k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)),k14_bvfunc_1(A,B,E)) ) ) ) ) ) )).

fof(t2_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k14_bvfunc_1(A,B,k8_bvfunc_1(A,k8_bvfunc_1(A,C,D),E)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)),k14_bvfunc_1(A,B,E)) ) ) ) ) ) )).

fof(t3_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E) = k8_bvfunc_1(A,k8_bvfunc_1(A,k14_bvfunc_1(A,B,E),k14_bvfunc_1(A,C,E)),k14_bvfunc_1(A,D,E)) ) ) ) ) ) )).

fof(t4_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k14_bvfunc_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),E) = k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,E),k14_bvfunc_1(A,C,E)),k14_bvfunc_1(A,D,E)) ) ) ) ) ) )).

fof(t5_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,B)) = k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,B)),k14_bvfunc_1(A,C,B)),k14_bvfunc_1(A,B,D)) ) ) ) ) )).

fof(t6_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => B = k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,k5_valuat_1(A,C))) ) ) ) )).

fof(t7_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => B = k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,B,k5_valuat_1(A,C))) ) ) ) )).

fof(t8_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => B = k8_bvfunc_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),k6_valuat_1(A,k6_valuat_1(A,B,C),k5_valuat_1(A,D))),k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),D)),k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) )).

fof(t9_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => B = k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),k5_valuat_1(A,D))),k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),D)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) )).

fof(t10_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k6_valuat_1(A,B,C) = k6_valuat_1(A,B,k8_bvfunc_1(A,k5_valuat_1(A,B),C)) ) ) ) )).

fof(t11_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k8_bvfunc_1(A,B,C) = k8_bvfunc_1(A,B,k6_valuat_1(A,k5_valuat_1(A,B),C)) ) ) ) )).

fof(t12_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k9_bvfunc_1(A,B,C) = k5_valuat_1(A,k15_bvfunc_1(A,B,C)) ) ) ) )).

fof(t13_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k9_bvfunc_1(A,B,C) = k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) ) ) ) )).

fof(t14_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k9_bvfunc_1(A,B,k19_bvfunc_1(A)) = k5_valuat_1(A,B) ) ) )).

fof(t15_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k9_bvfunc_1(A,B,k18_bvfunc_1(A)) = B ) ) )).

fof(t16_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k9_bvfunc_1(A,B,C) = k9_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) )).

fof(t17_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k5_valuat_1(A,k9_bvfunc_1(A,B,C)) = k9_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t18_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k15_bvfunc_1(A,B,C) = k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k8_bvfunc_1(A,k5_valuat_1(A,B),C)) ) ) ) )).

fof(t19_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k15_bvfunc_1(A,B,C) = k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) ) ) ) )).

fof(t20_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k15_bvfunc_1(A,B,k19_bvfunc_1(A)) = B ) ) )).

fof(t21_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k15_bvfunc_1(A,B,k18_bvfunc_1(A)) = k5_valuat_1(A,B) ) ) )).

fof(t22_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k5_valuat_1(A,k15_bvfunc_1(A,B,C)) = k15_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) )).

fof(t23_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => r1_bvfunc_1(A,k5_valuat_1(A,B),k15_bvfunc_1(A,k14_bvfunc_1(A,B,C),k5_valuat_1(A,B))) ) ) ) )).

fof(t24_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => r1_bvfunc_1(A,k5_valuat_1(A,B),k15_bvfunc_1(A,k14_bvfunc_1(A,C,B),k5_valuat_1(A,C))) ) ) ) )).

fof(t25_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => r1_bvfunc_1(A,B,k15_bvfunc_1(A,k15_bvfunc_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,C,B)),B)) ) ) ) )).

fof(t26_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k14_bvfunc_1(A,B,k15_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) )).

fof(t27_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => k14_bvfunc_1(A,k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),B),B) = k19_bvfunc_1(A) ) ) ) )).

fof(t28_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] :
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,E)),k8_bvfunc_1(A,k5_valuat_1(A,D),k5_valuat_1(A,E))),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) = k19_bvfunc_1(A) ) ) ) ) ) )).

fof(t29_bvfunc_8,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] :
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] :
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) )).
%------------------------------------------------------------------------------